# 特性黏度

${\displaystyle [\eta ]=\lim _{\varphi \rightarrow 0}{\frac {\eta -\eta _{0}}{\eta _{0}\varphi }}}$ 或者:${\displaystyle [\eta ]=\lim _{c\rightarrow 0}{\frac {\eta -\eta _{s}}{\eta _{s}c}}}$

## 刚性粒子

1906年，爱因斯坦讨论了刚性，之间无相互作用的球型粒子对溶液黏度的影响，发现溶液黏度与球型粒子的体积分数呈线性关系,即:${\displaystyle \eta =\eta _{s}(1+[\eta ]\varphi )}$ ,这被称为爱因斯坦方程，并且求出:${\displaystyle [\eta ]=5/2}$

## 哈金斯方程

${\displaystyle \eta =\eta _{s}(1+[\eta ]c+k_{H}[\eta ]^{2}c^{2}+\cdots }$

${\displaystyle {\frac {\eta }{\eta _{s}}}-1=[\eta ]c+k_{H}[\eta ]^{2}c^{2}+\cdots }$

${\displaystyle {\frac {\eta -\eta _{s}}{\eta _{s}c}}=[\eta ]+k_{H}[\eta ]^{2}c}$

## 实际应用与克莱默方程

${\displaystyle [\eta ]=\lim _{c\rightarrow 0}{\frac {\eta -\eta _{s}}{\eta _{s}c}}}$

${\displaystyle ln{\frac {\eta }{\eta _{s}}}=ln(1+[\eta ]c+k_{H}[\eta ]^{2}c^{2}+\cdots }$

${\displaystyle ln(1+x+kx^{2})=x+(k-1/2)x^{2}}$

${\displaystyle ln{\frac {\eta }{\eta _{s}}}=[\eta ]c+(k_{H}-{\frac {1}{2}})[\eta ]^{2}c^{2}+\cdots }$
${\displaystyle {\frac {ln{\frac {\eta }{\eta _{s}}}}{c}}=[\eta ]+(k_{H}-{\frac {1}{2}})[\eta ]^{2}c}$

## 参考文献

• 高分子物理，何曼君等人编著，复旦大学出版社，2008年
• Michael Rubinstein, Ralph H. Colby, Polymer Physics, 2004，Oxford University Press